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Total stability of kernel methods
- Source :
- Neurocomputing. 289:101-118
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
Abstract
- Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few hyperparameters or the kernel is even data dependent in a much more complicated manner. Examples are Gaussian RBF kernels, kernel learning, and hierarchical Gaussian kernels which were recently proposed for deep learning. Therefore, the actually used kernel is often computed by a grid search or in an iterative manner and can often only be considered as an approximation to the “ideal” or “optimal” kernel. The paper gives conditions under which classical kernel based methods based on a convex Lipschitz loss function and on a bounded and smooth kernel are stable, if the probability measure P, the regularization parameter λ, and the kernel K may slightly change in a simultaneous manner. Similar results are also given for pairwise learning. Therefore, the topic of this paper is somewhat more general than in classical robust statistics, where usually only the influence of small perturbations of the probability measure P on the estimated function is considered.
- Subjects :
- Cognitive Neuroscience
Hilbert space
Stability (learning theory)
010103 numerical & computational mathematics
Lipschitz continuity
01 natural sciences
Computer Science Applications
010104 statistics & probability
symbols.namesake
Kernel method
Artificial Intelligence
Kernel (statistics)
Hyperparameter optimization
symbols
Applied mathematics
Empirical risk minimization
0101 mathematics
Probability measure
Mathematics
Subjects
Details
- ISSN :
- 09252312
- Volume :
- 289
- Database :
- OpenAIRE
- Journal :
- Neurocomputing
- Accession number :
- edsair.doi...........9910e741aa4d17dcc8424810b82dd63a